(a) Find the moment of inertia \(I_{z z}\) of a thin disk of mass \(m\) and radius \(R\) about an axis through its center and perpendicular to the plane of the disk.

(b) What are \(I_{x x}\) and \(I_{y y}\) in this case?

(c) A solid cylinder of mass \(M\), radius \(R\), and length \(L\) can be considered to be a stack of disks. Use the parallel axis theorem to help find the principal moments of inertia of the cylinder whose origin is at the center of the cylinder.